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Proposition of Stochastic Postulates for Chain Indices

100%
Białek J.
Statistics in Transition new series
|
2014
|
vol. 15
|
issue 4
545_558
EN
This article presents and discusses a proposition of stochastic postulates for chain indices. The presented postulates are based on the assumption that prices and quantities are stochastic processes and we consider also the case when price processes are martingales. We define general conditions which allow the chain indices to satisfy these postulates.
2
Content available remote

A hybrid SETARX model for spikes in tight electricity markets

100%
LUCHERONI C.
Operations Research and Decisions
|
2012
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vol. 22
|
issue 1
13-49
EN
The paper discusses a simple looking but highly nonlinear regime-switching, self-excited threshold model for hourly electricity prices in continuous and discrete time. The regime structure of the model is linked to organizational features of the market. In continuous time, the model can include spikes without using jumps, by defining stochastic orbits. In passing from continuous time to discrete time, the stochastic orbits survive discretization and can be identified again as spikes. A calibration technique suitable for the discrete version of this model, which does not need deseasonalization or spike filtering, is developed, tested and applied to market data. The discussion of the properties of the model uses phase-space analysis, an approach uncommon in econometrics.
3
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Valuing managerial flexibility: An application of real-option theory to steel industry investments

88%
RĘBIASZ B., GAWEŁ B., SKALNA I.
Operations Research and Decisions
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2017
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vol. 27
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issue 2
91-111
EN
In the steel industry which is subject to significant volatility in its output prices and market demands for different ranges of products the diversification of production can generate important value for switch real options. Therefore, a common practice is to invest in various assets, thus generating the possibility of diversification of production and valuable switch options. The incremental benefit of product switch options in steel plant projects has been assessed. Such options are valued using the Monte Carlo simulation and modeling the prices of and demand for steel products as geometric Brownian motion (GBM). Our results show that this option can generate a significant increase in the net present value (NPV) of metallurgical projects.
4

Modelowanie matematyczne w muzyce na podstawie twórczości Iannisa Xenakisa

51%
Grębski T.
Roczniki Kulturoznawcze
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2019
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vol. 10
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issue 1
53-85
PL
Poszukiwanie matematycznych zależności w dziełach muzycznych to bardzo częste zjawisko badawcze. Można napotkać wiele utworów, w których artysta świadomie wykorzystywał wiedzę matematyczną podczas ich komponowania. Poszukiwanie matematycznych zależności w muzyce można by nazwać „matematyzowaniem muzyki”. Ale czy można „umuzycznić matematykę”, a dokładniej – obiekty matematyczne? W artykule analizie poddany jest problem „umuzyczniania matematyki”, zaś celem artykułu jest przedstawienie wybranych struktur matematycznych świadomie użytych przez Iannisa Xenakisa w kompozycjach. Jego twórczość jest doskonałym przykładem połączenia matematyki z muzyką. Mowa tu o procesach stochastycznych i rachunku prawdopodobieństwa, o teorii grup, o ruchach Browna i łańcuchach Markowa oraz o teorii gier. Muzyka Xenakisa przeciwstawiała się jakiejkolwiek tradycji w muzyce dzięki zastosowaniu w niej modelowania matematycznego. Była nieprzewidywalna, ale nie przypadkowa. W artykule mowa również o procesie twórczym przy komponowaniu muzyki oraz o matematycznym porządku w utworach muzycznych i walorach estetycznych i artystycznych. Artykuł ten dodatkowo ułatwi odbiór muzyki Xenakisa i pozwala lepiej zrozumieć jego twórczość.
EN
The search for mathematical relationships in musical compositions are often studied. There are many musical compositions, in which the composer consciously used mathematical knowledge during their composing. The search for mathematical dependence in music could be called “mathematization of music”. Can we use math to music illustration of mathematical objects? The problem of using music to math illustration is analyzed in this article and the aim of the article is to present some mathematical structures consciously used in the compositions by Iannis Xenakis. His work is an excellent example of the connection of mathematics with music. There are described stochastic processes and probability theory, group theory, game theory, and Brownian motion and Markov chains. Music of Xenakis opposed any tradition in music by using mathematical modeling in it. It was unpredictable, but not accidental. There is also about the creative process when composing music and about mathematical order in musical works, as well as aesthetic and artistic values. This article facilitates the perception of Xenakis music and enables to understand his work better.
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